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 A331947 Factors k > 1 such that the polynomial k*x^2 - 1 produces a record of its Hardy-Littlewood constant. 6
 2, 12, 20, 68, 90, 98, 132, 252, 318, 362, 398, 1722, 259668, 315180, 452042 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(16) > 710000. See A331940 for more information on the Hardy-Littlewood constant. The polynomials described by this sequence have an increasing rate of generating primes. The following table provides the record values of the Hardy-Littlewood constant C, together with the number of primes np generated by the polynomial P(x) = a(n)*x^2 - 1 for 2 <= x <= r = 10^8 and the actual ratio np*(P(r)/r)/Integral_{x=2..P(r)} 1/log(x) dx.     a(n)    C        np    C from ratio        2 3.70011  10448345 3.81422       12 4.15027  11154934 4.27219       20 4.43326  11753085 4.56136       68 5.01601  12883801 5.15797       .. .......  ........ .......   315180 7.82318  16502584 8.00057   452042 7.85323  16434699 8.02696 REFERENCES Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209. LINKS Karim Belabas, Henri Cohen, Computation of the Hardy-Littlewood constant for quadratic polynomials, PARI/GP script, 2020. Henri Cohen, High precision computation of Hardy-Littlewood constants, preprint, 1998. [pdf copy, with permission] CROSSREFS Cf. A221712, A331940, A331941, A331945, A331946, A331948, A331949. Sequence in context: A266050 A291698 A174478 * A145634 A145610 A185399 Adjacent sequences:  A331944 A331945 A331946 * A331948 A331949 A331950 KEYWORD nonn,more,hard AUTHOR Hugo Pfoertner, Feb 10 2020 STATUS approved

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Last modified June 16 13:58 EDT 2021. Contains 345057 sequences. (Running on oeis4.)